Solve 4^3/9-14(4^2/9+49*4/9-1/9frac{-14}{9}-frac{49}{9}

$$\frac{ { 4 }^{ 3 } }{ 9 } - \frac{ 14( { 4 }^{ 2 } }{ 9 } + \frac{ 49 \cdot 4 }{ 9 } - \frac{ 1 }{ 9 } \frac{ -14 }{ 9 } - \frac{ 49 }{ 9 }$$

Evaluate

$$-\frac{2777}{81}\approx -34.283950617$$

Solution Steps

Calculate 4 to the power of 3 and get 64.

$$\frac{64}{9}-\left(\frac{14\times 4^{2}}{9}+\frac{49\times 4}{9}-\frac{1}{9}\times \frac{-14}{9}-\frac{49}{9}\right)$$

Calculate 4 to the power of 2 and get 16.

$$\frac{64}{9}-\left(\frac{14\times 16}{9}+\frac{49\times 4}{9}-\frac{1}{9}\times \frac{-14}{9}-\frac{49}{9}\right)$$

Multiply 14 and 16 to get 224.

$$\frac{64}{9}-\left(\frac{224}{9}+\frac{49\times 4}{9}-\frac{1}{9}\times \frac{-14}{9}-\frac{49}{9}\right)$$

Multiply 49 and 4 to get 196.

$$\frac{64}{9}-\left(\frac{224}{9}+\frac{196}{9}-\frac{1}{9}\times \frac{-14}{9}-\frac{49}{9}\right)$$

Since \frac{224}{9} and \frac{196}{9} have the same denominator, add them by adding their numerators.

$$\frac{64}{9}-\left(\frac{224+196}{9}-\frac{1}{9}\times \frac{-14}{9}-\frac{49}{9}\right)$$

Add 224 and 196 to get 420.

$$\frac{64}{9}-\left(\frac{420}{9}-\frac{1}{9}\times \frac{-14}{9}-\frac{49}{9}\right)$$

Reduce the fraction \frac{420}{9} to lowest terms by extracting and canceling out 3.

$$\frac{64}{9}-\left(\frac{140}{3}-\frac{1}{9}\times \frac{-14}{9}-\frac{49}{9}\right)$$

Fraction \frac{-14}{9} can be rewritten as -\frac{14}{9} by extracting the negative sign.

$$\frac{64}{9}-\left(\frac{140}{3}-\frac{1}{9}\left(-\frac{14}{9}\right)-\frac{49}{9}\right)$$

Multiply \frac{1}{9} times -\frac{14}{9} by multiplying numerator times numerator and denominator times denominator.

$$\frac{64}{9}-\left(\frac{140}{3}-\frac{1\left(-14\right)}{9\times 9}-\frac{49}{9}\right)$$

Do the multiplications in the fraction \frac{1\left(-14\right)}{9\times 9}.

$$\frac{64}{9}-\left(\frac{140}{3}-\frac{-14}{81}-\frac{49}{9}\right)$$

Fraction \frac{-14}{81} can be rewritten as -\frac{14}{81} by extracting the negative sign.

$$\frac{64}{9}-\left(\frac{140}{3}-\left(-\frac{14}{81}\right)-\frac{49}{9}\right)$$

The opposite of -\frac{14}{81} is \frac{14}{81}.

$$\frac{64}{9}-\left(\frac{140}{3}+\frac{14}{81}-\frac{49}{9}\right)$$

Least common multiple of 3 and 81 is 81. Convert \frac{140}{3} and \frac{14}{81} to fractions with denominator 81.

$$\frac{64}{9}-\left(\frac{3780}{81}+\frac{14}{81}-\frac{49}{9}\right)$$

Since \frac{3780}{81} and \frac{14}{81} have the same denominator, add them by adding their numerators.

$$\frac{64}{9}-\left(\frac{3780+14}{81}-\frac{49}{9}\right)$$

Add 3780 and 14 to get 3794.

$$\frac{64}{9}-\left(\frac{3794}{81}-\frac{49}{9}\right)$$

Least common multiple of 81 and 9 is 81. Convert \frac{3794}{81} and \frac{49}{9} to fractions with denominator 81.

$$\frac{64}{9}-\left(\frac{3794}{81}-\frac{441}{81}\right)$$

Since \frac{3794}{81} and \frac{441}{81} have the same denominator, subtract them by subtracting their numerators.

$$\frac{64}{9}-\frac{3794-441}{81}$$

Subtract 441 from 3794 to get 3353.

$$\frac{64}{9}-\frac{3353}{81}$$

Least common multiple of 9 and 81 is 81. Convert \frac{64}{9} and \frac{3353}{81} to fractions with denominator 81.

$$\frac{576}{81}-\frac{3353}{81}$$

Since \frac{576}{81} and \frac{3353}{81} have the same denominator, subtract them by subtracting their numerators.

$$\frac{576-3353}{81}$$

Subtract 3353 from 576 to get -2777.

$$-\frac{2777}{81}$$

Factor

$$-\frac{2777}{81} = -34\frac{23}{81} = -34.28395061728395$$